Inhomogeneous Hypergraph Clustering with Applications
This work addresses hypergraph clustering for machine learning, computer vision, and network analytics, offering a novel approach that improves upon existing methods by considering inhomogeneous costs, though it is incremental in nature.
The paper tackles the problem of hypergraph partitioning by introducing inhomogeneous costs for different hyperedge cuts, which accounts for varying structural importance of vertex subsets. It proves a quadratic approximation guarantee under submodularity constraints and shows significant performance improvements in applications like ranking structure learning, subspace segmentation, and motif clustering.
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.